Details

Time bar (total: 7.8s)

analyze1.1s (13.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
3.5%96.2%0.2%10
9.8%89.9%0.2%11
14.1%85.7%0.2%12
22.6%77.1%0.2%13
23.7%76%0.2%14
Compiler

Compiled 19 to 12 computations (36.8% saved)

sample30.0ms (0.4%)

Algorithm
intervals
Results
8.0ms211×body128valid
2.0ms20×body512valid
1.0msbody1024valid
1.0ms13×body256valid
1.0ms20×body128invalid
1.0msbody2048valid
Compiler

Compiled 42 to 28 computations (33.3% saved)

simplify150.0ms (1.9%)

Algorithm
egg-herbie
Rules
1201×div-sub_binary64
620×sub-neg_binary64
553×unsub-neg_binary64
363×neg-mul-1_binary64 neg-sub0_binary64
307×distribute-rgt-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01219
12319
25819
313819
431519
584119
6180119
7310319
8331719
9363919
10375819
11402319
12421519
13487219

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
17.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
17.0b
(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
Compiler

Compiled 54 to 33 computations (38.9% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 (-.f64 z t) y)
3.1b
(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
11.8b
(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

rewrite141.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
9.5b
Rules
22×*-un-lft-identity_binary64
21×add-sqr-sqrt_binary64
11×cancel-sign-sub-inv_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64 times-frac_binary64
add-cube-cbrt_binary64
Counts
3 → 80
Calls

3 calls:

12.0ms
(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
10.0ms
(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
8.0ms
(*.f64 (-.f64 z t) y)
Compiler

Compiled 1626 to 341 computations (79% saved)

series257.0ms (3.3%)

Error
1.2b
Counts
3 → 76
Calls

3 calls:

109.0ms
(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
73.0ms
(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
28.0ms
(*.f64 (-.f64 z t) y)
Compiler

Compiled 3404 to 1855 computations (45.5% saved)

simplify138.0ms (1.8%)

Algorithm
egg-herbie
Rules
618×div-sub_binary64
473×cancel-sign-sub-inv_binary64
302×sub-neg_binary64
172×distribute-neg-frac_binary64
157×associate-/l*_binary64
Counts
156 → 133
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02623381
17863258
229873252
345863252
455153252

prune110.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New12013133
Fresh000
Picked101
Done000
Total12113134
Error
1.9b
Counts
134 → 13
Alt Table
StatusErrorProgram
32.0b
(-.f64 (+.f64 x y) (*.f64 (sqrt.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t)))) (sqrt.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))))
26.5b
(+.f64 (/.f64 (*.f64 y z) t) x)
39.3b
(-.f64 (+.f64 (/.f64 (*.f64 a (*.f64 a (*.f64 y z))) (pow.f64 t 3)) (+.f64 (/.f64 (*.f64 y z) t) (+.f64 (/.f64 (*.f64 a (*.f64 y z)) (*.f64 t t)) x))) (+.f64 (/.f64 (*.f64 y (pow.f64 a 3)) (pow.f64 t 3)) (+.f64 (/.f64 (*.f64 y a) t) (/.f64 (*.f64 y (*.f64 a a)) (*.f64 t t)))))
36.2b
(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 (*.f64 z z) (*.f64 t t)) y) (*.f64 (-.f64 a t) (+.f64 t z))))
23.7b
(+.f64 y x)
27.2b
(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 (*.f64 y a) t))
42.5b
(*.f64 (+.f64 (/.f64 (-.f64 z t) (-.f64 a t)) -1) (neg.f64 y))
13.0b
(+.f64 (+.f64 x y) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (neg.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))))
16.3b
(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))
39.2b
(/.f64 (-.f64 (*.f64 (+.f64 y x) (+.f64 y x)) (*.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))) (+.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))) (+.f64 y x)))
12.5b
(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
39.5b
(+.f64 (+.f64 x y) (*.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (neg.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t))))))
53.9b
(-.f64 (+.f64 x y) (/.f64 (*.f64 (/.f64 (-.f64 z t) (+.f64 (sqrt.f64 a) (sqrt.f64 t))) y) (-.f64 (sqrt.f64 a) (sqrt.f64 t))))
Compiler

Compiled 2414 to 748 computations (69% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 y (-.f64 a t))
4.6b
(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
9.8b
(*.f64 (-.f64 z t) (/.f64 y (-.f64 a t)))

rewrite156.0ms (2%)

Algorithm
rewrite-expression-head
Error
1.9b
Rules
44×add-sqr-sqrt_binary64
39×*-un-lft-identity_binary64
31×times-frac_binary64
23×add-cube-cbrt_binary64
21×associate-*r*_binary64
Counts
3 → 107
Calls

3 calls:

14.0ms
(*.f64 (-.f64 z t) (/.f64 y (-.f64 a t)))
8.0ms
(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
5.0ms
(/.f64 y (-.f64 a t))
Compiler

Compiled 2465 to 507 computations (79.4% saved)

series256.0ms (3.3%)

Error
1.2b
Counts
3 → 82
Calls

3 calls:

109.0ms
(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
69.0ms
(*.f64 (-.f64 z t) (/.f64 y (-.f64 a t)))
39.0ms
(/.f64 y (-.f64 a t))
Compiler

Compiled 3771 to 2081 computations (44.8% saved)

simplify170.0ms (2.2%)

Algorithm
egg-herbie
Rules
649×times-frac_binary64
282×sub-neg_binary64
190×distribute-rgt-in_binary64
180×distribute-lft-in_binary64
177×associate-*r*_binary64
Counts
189 → 138
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03174603
19274453
236294447
349764447
449734447

prune102.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1371138
Fresh3912
Picked011
Done000
Total14011151
Error
1.9b
Counts
151 → 11
Alt Table
StatusErrorProgram
26.5b
(+.f64 (/.f64 (*.f64 y z) t) x)
39.3b
(-.f64 (+.f64 (/.f64 (*.f64 a (*.f64 a (*.f64 y z))) (pow.f64 t 3)) (+.f64 (/.f64 (*.f64 y z) t) (+.f64 (/.f64 (*.f64 a (*.f64 y z)) (*.f64 t t)) x))) (+.f64 (/.f64 (*.f64 y (pow.f64 a 3)) (pow.f64 t 3)) (+.f64 (/.f64 (*.f64 y a) t) (/.f64 (*.f64 y (*.f64 a a)) (*.f64 t t)))))
36.2b
(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 (*.f64 z z) (*.f64 t t)) y) (*.f64 (-.f64 a t) (+.f64 t z))))
27.2b
(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 (*.f64 y a) t))
42.5b
(*.f64 (+.f64 (/.f64 (-.f64 z t) (-.f64 a t)) -1) (neg.f64 y))
12.7b
(-.f64 (+.f64 x y) (*.f64 (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t)))))
13.0b
(+.f64 (+.f64 x y) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (neg.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))))
16.3b
(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))
39.2b
(/.f64 (-.f64 (*.f64 (+.f64 y x) (+.f64 y x)) (*.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))) (+.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))) (+.f64 y x)))
12.5b
(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
53.9b
(-.f64 (+.f64 x y) (/.f64 (*.f64 (/.f64 (-.f64 z t) (+.f64 (sqrt.f64 a) (sqrt.f64 t))) y) (-.f64 (sqrt.f64 a) (sqrt.f64 t))))
Compiler

Compiled 2806 to 787 computations (72% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
3.5b
(*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t)))
6.3b
(*.f64 (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t))))
9.5b
(-.f64 (+.f64 x y) (*.f64 (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t)))))

rewrite478.0ms (6.1%)

Algorithm
rewrite-expression-head
Error
1.9b
Rules
340×cbrt-div_binary64
252×frac-times_binary64
172×flip3--_binary64 flip--_binary64
109×associate-*r/_binary64
106×frac-sub_binary64
Counts
4 → 306
Calls

4 calls:

28.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t))))
22.0ms
(-.f64 (+.f64 x y) (*.f64 (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t)))))
16.0ms
(*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t)))
12.0ms
(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
Compiler

Compiled 16834 to 2774 computations (83.5% saved)

series397.0ms (5.1%)

Error
1.9b
Counts
4 → 90
Calls

4 calls:

128.0ms
(-.f64 (+.f64 x y) (*.f64 (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t)))))
83.0ms
(*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t)))
80.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t))))
43.0ms
(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
Compiler

Compiled 5528 to 3125 computations (43.5% saved)

simplify471.0ms (6%)

Algorithm
egg-herbie
Rules
441×*-commutative_binary64
332×associate-*r*_binary64
316×distribute-rgt-in_binary64
308×distribute-lft-in_binary64
291×cancel-sign-sub-inv_binary64
Counts
396 → 363
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
083522760
1219121798
2466621761
3499221761

prune275.0ms (3.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3621363
Fresh279
Picked011
Done011
Total36410374
Error
1.2b
Counts
374 → 10
Alt Table
StatusErrorProgram
26.5b
(+.f64 (/.f64 (*.f64 y z) t) x)
39.3b
(-.f64 (+.f64 (/.f64 (*.f64 a (*.f64 a (*.f64 y z))) (pow.f64 t 3)) (+.f64 (/.f64 (*.f64 y z) t) (+.f64 (/.f64 (*.f64 a (*.f64 y z)) (*.f64 t t)) x))) (+.f64 (/.f64 (*.f64 y (pow.f64 a 3)) (pow.f64 t 3)) (+.f64 (/.f64 (*.f64 y a) t) (/.f64 (*.f64 y (*.f64 a a)) (*.f64 t t)))))
36.2b
(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 (*.f64 z z) (*.f64 t t)) y) (*.f64 (-.f64 a t) (+.f64 t z))))
27.2b
(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 (*.f64 y a) t))
12.7b
(-.f64 (+.f64 x y) (*.f64 (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t)))))
13.0b
(+.f64 (+.f64 x y) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (neg.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))))
16.3b
(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))
39.2b
(/.f64 (-.f64 (*.f64 (+.f64 y x) (+.f64 y x)) (*.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))) (+.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))) (+.f64 y x)))
12.5b
(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
38.8b
(neg.f64 (*.f64 y (-.f64 (/.f64 z (-.f64 a t)) (+.f64 (/.f64 t (-.f64 a t)) 1))))
Compiler

Compiled 11780 to 2582 computations (78.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (-.f64 a t))
0.5b
(cbrt.f64 (-.f64 a t))
3.7b
(*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (neg.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))
9.0b
(+.f64 (+.f64 x y) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (neg.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))))

rewrite232.0ms (3%)

Algorithm
rewrite-expression-head
Error
1.2b
Rules
48×add-sqr-sqrt_binary64
40×*-un-lft-identity_binary64
38×associate-*r*_binary64
36×times-frac_binary64
30×associate-*l*_binary64 cbrt-div_binary64
Counts
4 → 138
Calls

4 calls:

36.0ms
(*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (neg.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))
9.0ms
(+.f64 (+.f64 x y) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (neg.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))))
3.0ms
(cbrt.f64 (-.f64 a t))
3.0ms
(cbrt.f64 (-.f64 a t))
Compiler

Compiled 4978 to 781 computations (84.3% saved)

series552.0ms (7%)

Error
1.2b
Counts
4 → 77
Calls

4 calls:

300.0ms
(*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (neg.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))))))
122.0ms
(+.f64 (+.f64 x y) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (neg.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))))
38.0ms
(cbrt.f64 (-.f64 a t))
38.0ms
(cbrt.f64 (-.f64 a t))
Compiler

Compiled 5093 to 3066 computations (39.8% saved)

simplify172.0ms (2.2%)

Algorithm
egg-herbie
Rules
273×*-commutative_binary64
261×associate-*r*_binary64
238×associate-*l*_binary64
219×neg-sub0_binary64
210×neg-mul-1_binary64 associate-*r/_binary64
Counts
215 → 160
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04266545
112565753
244555750
350235750

prune152.0ms (1.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1591160
Fresh257
Picked011
Done022
Total1619170
Error
1.2b
Counts
170 → 9
Alt Table
StatusErrorProgram
39.3b
(-.f64 (+.f64 (/.f64 (*.f64 a (*.f64 a (*.f64 y z))) (pow.f64 t 3)) (+.f64 (/.f64 (*.f64 y z) t) (+.f64 (/.f64 (*.f64 a (*.f64 y z)) (*.f64 t t)) x))) (+.f64 (/.f64 (*.f64 y (pow.f64 a 3)) (pow.f64 t 3)) (+.f64 (/.f64 (*.f64 y a) t) (/.f64 (*.f64 y (*.f64 a a)) (*.f64 t t)))))
27.2b
(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 (*.f64 y a) t))
12.7b
(-.f64 (+.f64 x y) (*.f64 (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (*.f64 (/.f64 y (-.f64 a t)) (cbrt.f64 (-.f64 z t)))))
13.0b
(+.f64 (+.f64 x y) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (neg.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))))))
16.3b
(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))
39.2b
(/.f64 (-.f64 (*.f64 (+.f64 y x) (+.f64 y x)) (*.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))) (+.f64 (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))) (+.f64 y x)))
12.5b
(-.f64 (+.f64 x y) (*.f64 (-.f64 z t) (/.f64 y (-.f64 a t))))
9.3b
(+.f64 x (-.f64 y (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))))
38.8b
(neg.f64 (*.f64 y (-.f64 (/.f64 z (-.f64 a t)) (+.f64 (/.f64 t (-.f64 a t)) 1))))
Compiler

Compiled 3896 to 945 computations (75.7% saved)

regimes1.4s (17.8%)

Accuracy

Total 5.0b remaining (85.2%)

Threshold costs 0b (0%)

Compiler

Compiled 16835 to 9048 computations (46.3% saved)

bsearch4.0ms (0.1%)

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify10.0ms (0.1%)

Algorithm
egg-herbie
Rules
18×+-commutative_binary64
15×sub-neg_binary64
13×*-commutative_binary64
11×neg-mul-1_binary64 neg-sub0_binary64
distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02988
14788
26888
39688
412388
513788
614088
713688

end1.0ms (0%)

Compiler

Compiled 64 to 28 computations (56.3% saved)

sample1.1s (13.6%)

Algorithm
intervals
Results
278.0ms6690×body128valid
64.0ms501×body512valid
57.0ms389×body1024valid
32.0ms358×body256valid
31.0ms783×body128invalid
16.0ms62×body2048valid
Compiler

Compiled 344 to 176 computations (48.8% saved)

Profiling

Loading profile data...